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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 488 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is 67²? =
  3. 3.A square garden has an area of 361 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 8² and 9²?
  5. 5.Which of these is a perfect square? (a) 676 (b) 704 (c) 712
  6. 6.What is √6400? =
  7. 7.A square garden has an area of 576 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 24² and 25²?
  10. 10.What is √9604? =
  11. 11.What is 14²? =
  12. 12.A square garden has an area of 441 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 47² and 48²?
  15. 15.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √9216? =
  17. 17.What is 46²? =
  18. 18.What is the smallest whole number by which 245 must be divided to get a perfect square?
  19. 19.What is 79²? =
  20. 20.Which of these is a perfect square? (a) 410 (b) 400 (c) 404
  21. 21.A square garden has an area of 256 square m. How long is each side (in m)?
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 72 must be divided to get a perfect square?
  24. 24.Which of these is a perfect square? (a) 220 (b) 219 (c) 196
  25. 25.How many whole numbers lie between 13² and 14²?
  26. 26.How many whole numbers lie between 36² and 37²?
  27. 27.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  28. 28.Which of these is a perfect square? (a) 575 (b) 529 (c) 534
  29. 29.What is √484? =
  30. 30.A square garden has an area of 729 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 637 must be divided to get a perfect square?
  32. 32.How many whole numbers lie between 20² and 21²?
  33. 33.What is 43²? =
  34. 34.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  35. 35.What is 21²? =
  36. 36.What is the smallest whole number by which 75 must be divided to get a perfect square?
  37. 37.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is 36²? =
  39. 39.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  40. 40.How many whole numbers lie between 44² and 45²?

Answer key

  1. 36
  2. 4489
  3. 19
  4. 16
  5. 676
  6. 80
  7. 24
  8. 361
  9. 48
  10. 98
  11. 196
  12. 21
  13. 15
  14. 94
  15. 121
  16. 96
  17. 2116
  18. 5
  19. 6241
  20. 400
  21. 16
  22. 144
  23. 2
  24. 196
  25. 26
  26. 72
  27. 5
  28. 529
  29. 22
  30. 27
  31. 13
  32. 40
  33. 1849
  34. 15
  35. 441
  36. 3
  37. 784
  38. 1296
  39. 7
  40. 88

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